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Searching for Global Consciousness – Supplementary Materials

S.1 Introduction!1

S.2 GCP Data Structure!1

S.3 Data Vetting and Normalization!2

S.4 Network Deployment!4

S.5 Event Structure!6

S.5 Test statistics!7

S.7 Formal Result!10

S.8 XOR processing for Mindsong and Orion RNGs!12

S.9 Network synchronization!13

S.10 Counterfactual test 1: Undesignated surrogate events!15

S.11 Counterfactual test 2: Alternate test statistics!16

S.12 Hypothesis intervention 1: Fine-tuning of the variance statistic!16

S.13 Hypothesis intervention 2: Fine-tuning to correlation timestamps!18

S.14 Evidence for anomalous data selection!18

S.1 Introduction

This document gives a technical overview the GCP network, database and formal

experiment, as well as details of some analyses presented in the main paper. The

discussion pertains to all data since the commissioning of the GCP network on August 5,

1998 through May 31, 2015. The database comprises 6139 consecutive days and 26.02

billion data trials (data is missing for August 5-8, 2002, due to a network failure during

those days).

S.2 GCP Data Structure

The GCP data ﬁles are archived in comma-separated values (CSV) format available for

download from the GCP website : http://teilhard.global-mind.org/extract.html (accessed

Jan 6, 2016). Files contain data for 24 hour UTC days and list, in separate records, the

data trials from online RNGs for each second of the day. Further information on the ﬁle

structure is available at http://teilhard.global-mind.org/basket_CSV_v2.html .

Data trials are sums of 200 consecutive bits output from each RNG in the global network.

Bits are collected locally via a serial port interface at the start of each second (as

determined by the computer clock of the local host) and summed to yield a binomial datum

B[200, 0.5], with nominal mean values and standard deviations of 100 and √50,

respectively. After the 200 bits are collected, the acquisition sleeps until the next second,

discarding all bits produced by the RNG during sleep time. The bit generation rates are

approximately 2600/sec and 8000/sec for the Mindsong and Orion RNGs, so that roughly

95% of all generated bits are discarded.

S.3 Data Vetting and Normalization

Data Normalization.

For analyses, it is convenient to convert the binomial trials to standard normal scores (z-

scores) with means of 0 and variance 1. The RNGs deployed in the network are known to

have small, stable biases in their means and variances. The standardization is thus done

separately for each device using the empirically determined mean and variance values of

the binomially distributed data trials.

The normalization is most important for the Mindsong RNGs which have substantial

variance biases (Figure 1). Normalizations are carried out periodically (typically once a

year). The updating of empirical means and variances are calculated using all data from

each RNG to date. However, the normalization is CPU intensive (there are roughly 2 billion

trial bitsums in a year's worth of data) and previously treated data are not re-normalized.

Thus, over the course of the experiment, the normalization parameters for each RNG

evolve somewhat. This results in overall normalizations that deviate slightly from the exact

standard values of 0 and 1 for the normalized means and variances (Figure 2). The

normalization variability is small and does not impact analyses that may assume exact

standardization of the trials.

Data Vetting.

Aside from the stable, characteristic biases of each device, the RNGs occasionally

produce bad trial values or additional biases for limited periods. These are usually due to

instabilities in the power supplied to the devices through the serial port interfaces. A three

step procedure is used to vet and remove periods of bad RNG data.

First, power glitches occasionally cause extreme binomial values (most often long strings

of 0 values). Individual binomial trials that lie outside the range [55, 145] are removed. The

range is selected so that only a handful of good data trials will be excluded. The vetting

removes 307,006 bad trials (about 1 in 100,000). All except 3 of the trials lie far outside the

exclusion range.

The second step performs ﬁrst-pass vetting using a standard normalization

and searches for data, in month-long blocks for each RNG, with means or variances far

exceeding what would be expected from the typical characteristic biases. The bad data

months are masked and empirical means and variances are calculated from the remaining

data individually for each RNG. The full database is then normalized using the empirical

values. A vetting program then searches for bad data blocks on timescales ranging from 1

minute to 3 months, identifying blocks with means or variances that lie outside an

appropriate cutoff. The cutoff range for each blocking is set so that an inconsequential

fraction of good data blocks will be identiﬁed by the procedure.

The third step re-calculates empirical RNG means and variances with bad data blocks

removed. The full database is normalized with these values and passed to the vetting

program to yield a ﬁnal list of bad data blocks. The bad blocks are then removed from the

database. In all, 69 bad blocks of various durations were identiﬁed for 19 of 141 data-

producing RNGs.

z=(bitsum µRng)/Rng

z=(bitsum 100)/p50

Null trials.

Aside from bad data, RNG nodes produce a substantial number missing (null) values. This

has no statistical impact on the database, but needs to be managed for some analyses

(such as autocorrelations) since the resulting data matrices are in general slightly sparse

and consecutive seconds of data can contain differing numbers of trials. Approximately

3.9% of collected data trials are null.

The normalization can be validated by examining the ﬁrst four moments of the trial

distribution. Theoretically the mean, variance, skewness and kurtosis should have values

[0,1,0, 2.99] (the kurtosis retains its binomial value after normalization). The values for the

normalized database are found to be [-0.000003, 1.00000, 0.000001, 2.98995], in good

agreement with the theoretical values.

Figure 1. Raw variances of individual RNGs in the GCP database. The binomial trials have been

normalized using theoretical mean and variance values of the B[200,0.5] distribution. Vertical

bars show one standard error and vary for each RNG according to the number of trials

collected. Blue and red points indicate the Orion and Mindsong devices, respectively. The need

for empirical normalization is evident from by the large number of variances that deviate

strongly from the expected value of 1. Nearly all of the RNGs with signiﬁcant biases are

Mindsongs.

Figure 2. Trial variances after empirical normalization. The small scatter of values about the

ideal of 1 is due to periodic updating of normalization parameters and the statistical nature of

the algorithm for vetting bad data.

S.4 Network Deployment

The GCP has deployed 141 data producing RNGs over the course of the experiment.

Although the coverage is global, most nodes are concentrated in Europe and North

America. Contributions to the database from each node vary widely, as shown in Figure 6.

Four different commercial RNGs have been used by the GCP (trade names Mindsong,

Orion, Araneus and TruRNG). The Mindsong and Orion RNGs comprise most of the

network and are deployed in roughly equal numbers. The number and location of nodes

changes over time depending on the availability of the volunteer hosts. As a consequence,

the data for events is drawn from a constantly changing network conﬁguration. Figure 7

shows the total number of online RNGs for each event and the relative contributions from

different RNG types.

Figure 4. Location of nodes in the GCP network showing all 137 RNGs that have contributed at

least a month's worth of data. Green points indicate nodes that have produced data for a total of

2 years or more during 17 years of operation through May 2015.

Figure 5. Detail of the GCP network showing the concentration of nodes in North America and

Europe. All nodes shown have produced more than a month of data. Green nodes have

produced data for 2 years or more and orange nodes for 10 years or more.

Figure 6. Data contributions for 141 data-producing RNGs. The vertical axis expresses the data

contributions as equivalent non-null data-years. The number of binomial trials in a data-year

equals the number of seconds in a year. The Figure shows that many RNGs make relatively

minor contributions to the database. The max/min contributions are 16.3 years and 14 hours.

Figure 7. Counts of the data-producing online network RNGs for each formal event. Blue trace:

the total RNG count; red trace : Mindsong RNGs only; black trace: Araneus RNGs only (4

Araneus RNGs were deployed in 2011). Network deployment peaked in 2010-2011 and has

declined since. The short-term variability in the number of online RNGs is due to devices

coming ofﬂine or producing nulls for long periods.

S.5 Event Structure

Event durations.

Event periods vary from 1 minute to 10 days, but most durations are from 1 to 24 hours.

Figure 8. Distribution event durations. Most event periods last for ≤ 12 hours and roughly 20%

have durations of 24 hours. Eight events with durations of several days are not shown.

Figure 9. Relative fractions of data trials for subsets of event durations. The 97 day-long events

account for half of the event data, whereas 337 events with durations ≤ 12 hours comprise only

a third of all event data.

S.5 Test statistics

Event z-scores and the GCP cumulative result

The GCP has used different statistics to test formally registered events. To present a

cumulative result for the experiment, event tests are converted to standard normal z-

scores, which are then averaged with equal weighting. Each event thus contributes equally

to the average, regardless of the duration or the total number of trials in the event period.

The signiﬁcance of the cumulative result is determined by the standard error of the mean

of the average event z-score, relative to the null hypothesis of zero. The cumulative result

is often given as an overall z-score for the experiment (which is easily converted to a

probability value).

Rejected events

Thirteen events are excluded from the experiment due to methodological issues. These

include ambiguous event speciﬁcations or inadvertent data peeking that potentially

compromise the integrity of event z-score calculations. Notably, the U.S. terror attacks of

September 11, 2001 is one of the rejected events since the data was brieﬂy examined

before the event period was fully determined. The GCP event IDs for the rejected events

are : (2, 10, 17, 18, 19, 30, 33, 34, 38, 44, 66, 81, 116)

Multiple period events

Most events designate a single time period. However, 54 events span multiple non-

contiguous periods. Of these, 34 are New Year's Eve events that specify short periods

around midnight across different time zones. In most cases the periods are combined to a

single contiguous data set that is treated as a single event.

Event hypothesis tests

Nine different statistics have been used to test events against the GCP hypothesis. Of the

491 valid events treated in this paper, 418 (85%) use a standard method. The other

statistics are used in special circumstances. Examples are 28 early events discussed in

the counterfactual test 2 of the paper, and the 17 New Year's Eve events which are

measured twice with two independent statistics (giving 34 event tests in total).

All but three statistics (one of the New Year's statistics and 3 others that were each used

on a single event) test a measure of the data trials' variance, with the hypothesis prediction

being that the variance will increase under the inﬂuence of a global consciousness effect.

The procedure is to group or block the data trials into subsets and calculate a z-score for

the data blocks. The the variance of the block z-scores is then calculated as a chi-squared

test statistic. The general procedure can be written as:

zexperiment =

1

pN

Nevents

X

n=1

zevent

zblock =

1

pNtrials

Ntrials

X

n=1

zn

2

blocks =

Nblocks

X

b=1

z2

b

The block variance is proportional to the chi-squared statistic which has degrees of

freedom (df) equal to the number of blocks. Following standard procedure, the probability

value of the chi-squared statistic can be calculated with the regularized incomplete gamma

function:

Finally, the chi-squared P-value is converted to a z-score for the event via the inverse error

function:

Event statistics

The variance statistics differ in the way that the data are blocked to yield block z-scores. In

general, the normalized data for an event is a matrix of trial z-scores, z(r, t), with r denoting

the RNG and t the timestamp of the trial. The blocking schemes used by the GCP are

described below. Consider that there are N online RNGs and T seconds in an event.

1-Second blocking: the standard analysis. The standard analysis (418 events) blocks trials

over all N RNGs for each second. The df is equal to the total number of seconds in the

event period, T.

RNG blocking. The variance analysis of 28 early events blocks trials from the N RNGs

individually into 15-minute segments (900 seconds) (One additional event blocks RNGs

into 10-minute segments.). An index, b, enumerates the 15-minute blocks and df = b*N.

P value =(df

2,2

2)

(df

2)

zevent =p2(erf )1[0,12Pvalue]

zt=

1

pN

N

X

r

zr,t

2

df =

T

X

t

z2

t

zr,b =1

p900

900

X

tb=1

zr,t

2

df =

N,B

X

r,b

z2

r,b

Minute blocking. Five long events block all RNGs together in 1-minute blocks. The df is

equal to the total number of minutes in the event period.

Epoch multi-period events. Seventeen New Year's and 5 additional events designate non-

contiguous multiple periods of equal durations. The events typically entail an observance

that is repeated locally in different places and times. An example is the New Year, which

speciﬁes 10-minute periods around midnight in each of 36 world time zones. In a sense,

the epoch blocking treats the periods as occurring simultaneously by summing over all

RNGs and epochs for each second of the epoch durations. Indicating the number of

epochs as P, and the epoch index as p, the procedure is written as

Correlation statistic. It is useful point out that the standard analysis can be written in terms

of simultaneous RNG-RNG pair correlations and the trial variance:

zm=1

p60N

tm=60

X

tm,r

zr,t

2

df =

M

X

m

z2

m

zt=

1

pN⇤P

N,P

X

r,p

zr,t,p

2

df =

TEpoch

X

t

z2

t

where the correlation, ρ, is the average product of all pairs of RNG trials taken at equal

times:

and the chi-squared df is identiﬁed as T, the total seconds in the event. Because the

coefﬁcient (N-1) is on the order of 50, the correlations will dominate deviations in the chi-

squared statistic. To a good approximation, the effect measured for standard analysis

events appears almost entirely as correlations between RNGs. The correlation has an null

expectation of zero and a standard error, σ, determined by the total number of pair-

products. The measured average correlation for standard analysis events is ~0.00004. It is

possible to write a correlation z-score as z = ρ/σ because the pair products, z*z, distribute

as a random variable with a ﬁnite variance and the large number of terms in the correlation

sum satisﬁes the Central Limit theorem.

If correlation z-scores are used to calculate the cumulative result for the 418 standard

analysis events alone, a cumulative z-score of 6.35 obtains. Using the standard analysis,

the event z-scores combine to a value of 6.46, which conﬁrms that the effect is essentially

due to pair correlations of the RNG outputs taken at equal times.

S.7 Formal Result

The GCP event experiment yields a highly signiﬁcant cumulative result. The overall

experimental z-score stands at 7 standard deviations from the null hypothesis. The event

effect size (the average event z-score) is 0.316 ± 0.045. A cumulative sum of the event z-

scores is shown in Figure 10.

2

df =

T

X

t 1

pN

N

X

r

zr,t !2

=1

N

T

X

t

N

X

i,j

zi,tzj,t

=1

N

T

X

t0

@

N

X

i

z2

i+

N

X

i6=j

zi,t ⇤zj,t1

A

=T⇣z2+(N1)zizj⌘

2

df

df =2

z+(N1)⇢,

⇢=zi(t)zj(t)

z⇢=

⇢

⇢

=

⇢

qN(N1)T

2

The full database does not exhibit the anomalous deviations seen during events. Figure 11

shows the cumulative distribution of z-scores calculated using the standard analysis for

each day from January 1, 2000 to May 31, 2015. Days that include events have been

removed, so that only non-event data is used. The cumulative remains within a 0.05

probability envelope and is consistent with the null hypothesis of no global consciousness

effect.

Figure 10. Cumulative sum of z-scores for 491 formal events. The average event z is 0.316 and

the cumulative z-score is 7.01 which yields a P-value of 10-12. The gray traces show probability

envelopes of 0.05 and 0.001.

Figure 11. The cumulative distribution of daily standard analysis z-scores for the database. Days

that include events have been excluded. The gray trace is a 0.05 probability envelope. The

cumulative exhibits behavior consistent with the null hypothesis and shows no global

consciousness effect.

S.8 XOR processing for Mindsong and Orion RNGs

As discussed in the paper, raw bits from the Orion and Mindsong RNGs are processed

with an exclusive-or (XOR) before being summed into 200-bit trials. The XOR algorithm

compares raw bits output by the RNG to a sequence of XOR bits. The ﬁnite XOR bit

sequence (the XOR mask) cycles continuously during the procedure. The masks are

balanced, with an equal number of 0 and 1 bits, and the algorithm inverts raw bits when

the mask bit is 1. A mask bit of 0 leaves the raw RNG bit unchanged. The procedures for

Orion and Mindsong devices are as follows.

Orion XOR

The Orion device contains two identical, internal RNGs. The two bit streams are XOR'd

against each other and passed to the RNG output. Each bit stream is thus effectively

subject to a truly random XOR mask. The Orion device cannot insure that ﬁrst order biases

will be eliminated by the mutual XORing of internal RNGs because the individual bit

streams may be biased. In this case, the effective mask that is the alternate bit stream will

not be balanced and biases can be passed to the output. Biases will be eliminated if at

least one of the internal RNGs is unbiased, but there is no guarantee that will be the case.

For this reason, the Orion RNG outputs are subject to an additional XOR by the data

acquisition software. The software mask is a 2-bit 01 sequence that cycles over the input

bits before they are summed to trials.

Two further points are noteworthy. First, the ﬁnal software XOR is synchronized to the

computer clock of the local network host. Accordingly, the Orion XORs can in principle be

synchronized across the GCP network since the computer clocks are synchronized via

Internet time protocols. The required accuracy for synchronizing XORs across the network

is thus given by the bit generation time. For the Orion devices which operate close to 9600

baud, the required accuracy is on the order of 100 micro-seconds.

The second point is that the internal XORing renders the Orion devices potentially more

susceptible to network correlations of the type envisioned by the GCP. As discussed in the

paper, correlations will be measured only if both the XORs and the raw bit streams are

correlated. For the raw bits, this requires that two distant RNGs produce equal raw bit

sequences simultaneously. However, in the case of the Orion devices this stringent

condition is relaxed somewhat because any bit XOR'd against itself results in an output bit

of 0. If an effect were to cause both internal RNGs to produce identical bit sequences, the

output after mutual XORing would be a string of 0 bits. Two Orion devices could thus

produce simultaneous 0 bit sequences as long as the two pairs of internal RNGs each

produced identical raw bits locally. But there is no requirement that those raw sequences

also be identical at the two locations.

Mindsong XOR

The Mindsong device uses an internal balanced mask to XOR bits from a single RNG bit

stream. Because the mask is balanced, there is no software XOR procedure for network

nodes with Mindsong devices. The bit generation rate is approximately 2600 bits/sec and

is maintained by an internal timer. The timer clock runs independently of the computer

host, so that there is no possibility of synchronization among the Mindsong XOR masks in

the network.

The Mindsong XOR mask is a concatenation of the 70 unique permutations of the

balanced 8-bit sequence (0,0,0,0,1,1,1,1). The mask was designed to minimize

autocorrelations on the length scale of 200 bits (the Orion software 01 XOR has, obviously,

a strong autocorrelation as it cycles over bits). The concern is that autocorrelations can

lead to the increased variance of bit-summed trials. However, the mask design does not

appear to be adequate, at least for the internal RNG included in the devices, since most of

the deployed Mindsong RNGs exhibit signiﬁcant variance excesses before normalization.

The exact sequence of the 560-bit Mindsong mask is listed below:

(1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0,

1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0,

1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0,

1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1,

1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1,

1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0,

1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0,

1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1,

0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1,

1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0,

0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0,

1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0,

0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1,

1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0,

0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1,

0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1)

S.9 Network synchronization

It is helpful to sketch some details of the synchronization problem. Computer clocks are

subject to timing and frequency drifts from temperature changes, processor loads and

other factors and these result in timing offsets that need to be corrected periodically.

Corrections are made by software algorithms that compare the internal clocks to stable

time servers available on the Internet. The GCP employs two standard protocols for its

network synchronization (NTPv3; Network Time Protocol version 3, and Win32Time on

some older Windows operating systems). Over the course of the Project's operation,

roughly 140 nodes have been deployed at one time or another. Of these, 44 used the

Win32Time protocol, a rather poor protocol that has an accuracy of one or two seconds at

best1. The NTPv3 protocol, in principle, can achieve synchronization to an accuracy of

several milliseconds under ideal conditions. But this is an order of magnitude weaker than

what is required for GC ﬁeld models, and the actual timing in the global network is far

worse than the optimal performance of NTP. The main factors that degrade the

synchronization are query latencies with the time servers and conditions at the local

computers. Conditions are less than ideal in the GCP network which has nodes in a wide

range of locations, some remote, and uses older computers due to the need for serial port

interfaces. In addition, over its 17 years of operation the GCP has not monitored the NTP

daemons at the local nodes to ensure that they are running correctly and that they

maintain adequate polling of the time servers. All of these factors have serious implications

for network synchronization. The conclusion is that any effect that might produce

synchronized correlations among raw bits will be destroyed by timing offsets that

randomize the XOR mask phases. Hence the conclusion that a GC ﬁeld model cannot

account for the correlations measured by the experiment.

Although no record of node synchronization has been kept by the GCP, a real-time

veriﬁcation of the trial timestamps was made in 2013 which allowed a check at the limited

resolution of 1 second. The timestamps were veriﬁed at one minute intervals over a period

1 Microsoft Corporation Support documentation: https://support.microsoft.com/en-us/kb/939322

of roughly an hour, and the veriﬁcation was repeated for 24 days. It was found that 52 of

60 online nodes exhibited timestamp offsets of one second or more, with 17 exhibiting

offsets exceeding a minute. Thus, at a gross resolution of 1 second, timestamp accuracy

could be veriﬁed at only 13% of the nodes, implying that less than 2% of the node pairings

could assure synchronization to within one second, an accuracy which is itself orders of

magnitude below the criterion for XOR synchronization. In addition, the timing offsets are

not stable. The nodes with offsets all drifted by a second or more over the course of an

hour during most test periods. The drift rates are greater than 100 microseconds per

second, which means that the network de-synchronizes beyond the correlation criterion in

about one second. Nor do the subset of nodes with better synchronization yield stronger

correlations. The correlations over all events for 15 nodes that maintained better than 95%

synchronization at the 1-second level during the 2013 test produced average event data

correlations slightly below the rest of the network, with the difference being within a

standard deviation of expected noise.

S.10 Counterfactual test 1: Undesignated surrogate events

The test of self-referential ﬁne-tuning (SFT) compares 15 registered 24-hour UTC day

events for Earth Day and International Peace Day celebrations with 15 unregistered

surrogate events. The GCP event IDs, and dates of the registered events are listed in the

Table, followed by the unregistered surrogate events. The Earth Day of 2015 is excluded

from the surrogate set since the GCP registered another event for most of that day.

GCP Event ID

Event

Date

Event z-score

73

Earth Day

April 22, 2001

-1.45

185

Peace Day

Sept. 21, 2004

-0.86

216

Earth Day

April 22, 2006

0.00

250

Peace Day

Sept. 21, 2007

1.65

261

Earth Day

April 22, 2008

-0.49

276

Peace Day

Sept. 21, 2008

3.09

294

Earth Day

April 22, 2009

1.09

307

Peace Day

Sept. 21, 2009

0.46

331

Earth Day

April 22, 2010

3.16

345

Peace Day

Sept. 21, 2010

1.60

374

Earth Day

April 22, 2011

1.32

391

Peace Day

Sept. 21, 2011

0.59

429

Peace Day

Sept. 21, 2012

0.06

465

Peace Day

Sept. 21, 2013

-0.19

487

Peace Day

Sept. 21, 2014

0.10

Registered events cumulative Z : 2.61

Registered events cumulative Z : 2.61

1

Earth Day

April 22, 2000

1.78

2

Peace Day

Sept. 21, 2000

0.95

3

Peace Day

Sept. 21, 2001

-1.34

4

Earth Day

April 22, 2002

0.84

5

Peace Day

Sept. 21, 2002

-1.00

6

Earth Day

April 22, 2003

0.67

7

Peace Day

Sept. 21, 2003

-0.15

8

Earth Day

April 22, 2004

0.53

9

Earth Day

April 22, 2005

0.36

10

Peace Day

Sept. 21, 2005

-0.26

11

Peace Day

Sept. 21, 2006

0.65

12

Earth Day

April 22, 2007

-0.66

13

Earth Day

April 22, 2012

-0.49

14

Earth Day

April 22, 2013

-0.94

15

Earth Day

April 22, 2014

-1.25

Surrogate events cumulative Z : -0.08

Surrogate events cumulative Z : -0.08

S.11 Counterfactual test 2: Alternate test statistics

The second counterfactual demonstration of SFT shows that a test statistic yields an effect

only when assigned to an event. When applied to other events that formally designate a

different statistic, the ﬁrst test statistic returns a null result. Some additional details of the

comparison are given here. The demonstration identiﬁes 3 events subsets that designated

different, independent test statistics. The cumulative z-score for each subset is calculated

using each of the 3 statistics. The subsets are 4 events with minute blocking, and 28

events with RNG blocking (see S.5). The third is a truncated subset of the standard

analysis events. Some standard analysis events have event durations that do not permit

an exact application of the 15-minute RNG blocking (events that are 20 minutes long, for

example). They are dropped if shorter that 4 hours and retained otherwise.

Table 2 shows the details of the analysis. The ﬁrst two rows are reproduced from the

paper, which combines the RNG and minute blocked subsets. For completeness, a

breakdown of the individual subsets is also given.

The 3 statistics are not exactly independent, but their correlations are insigniﬁcant for the

purposes of the demonstration. This has been conﬁrmed by simulation, but it is also

obvious by inspecting the blocking speciﬁcations given in section S.5.

The event IDs for the RNG blocked events are: (1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16,

21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 35, 36, 37, 39).

IDs for the minute blocked events are : (46, 51, 53, 79).

S.12 Hypothesis intervention 1: Fine-tuning of the variance statistic

The hypothesis intervention shows that cumulative z-scores of an event subset tune to the

blocking selected by the hypothesis prediction. The intervention combines subsets of 4

minute blocked with 28 RNG blocked events and scales changes in the block duration in a

consistent way across the two subsets. The minute blocking durations are varied from 1 to

120 seconds. Durations for 15-minute RNG blocked events vary from 1 to 30 minutes.

The model assumes that correlations are tuned to the designated block size (15 or 1

minutes, respectively) and are homogeneously distributed within the blocks. The event z-

score is thus given by the average correlation multiplied by the square root of the number

of trial pair-products. For blockings at times shorter than the original, the average

correlation is unchanged since all sub-blocks remain within the original designated block.

However, the shorter blocking reduces the total number of pair-products which causes the

measured z-score to decrease.

Standard Z

RNG blocking Z

Minute blocking Z

N events

Standard events

6.90 (0.33)

-0.59 (-0.03)

-0.85 (-0.04)

448

RNG & minute events

0.23 (0.04)

2.59 (0.46)

0.50(0.09)

32

RNG blocked events

0.09 (0.02)

2.74 (0.52)

-0.07 (-0.01)

28

Minute blocked events

0.40 (0.20)

0.08 (0.04)

1.59 (0.80)

4

Table 2. Comparison of two alternate GCP hypothesis tests with their formal event

assignments. The table lists the standard deviation (as a Stouffer Z statistic) for each group

along with the average event z-score (in parentheses). Numbers in boldface are the formal

tests reported by the GCP. The Stouffer Z is found to be signiﬁcant only when the statistic is

formally designated and is non-signiﬁcant when calculated for events that originally

designated an alternate statistic, in agreement with STF.

Blocking at times longer than the original designation increases the total number of pair-

products, but this is offset by mixing pair-products across the originally designated blocks.

Since these are uncorrelated, the average correlation decreases, resulting in a slow

decline of the measured z-scores as the block size grows.

With a normalized original block size of B0=1, an original average pair-product μ0, and

taking the number of pair-products in any block as df (and in the approximation that the

number of seconds in B0 is much greater than 1), the model is expressed as :

zevent =µ0pdf

Blocksize B < B0

µblock =µ0

df B=✓B0

B◆B2=B0B

zB=µ0pB0B

Blocksize B > B0

µblock =µ0

B0+(BB0)2

B2

df B=B0B

zB=µblock pB0B

=µ0pB0 B0+(BB0)2

B3

2!

S.13 Hypothesis intervention 2: Fine-tuning to correlation timestamps

Fine-tuning to erroneous timestamps is demonstrated by simulating a decrease of the

timestamp alignments. As predicted by SFT, the z-scores for the 414 standard events

depend linearly on the degree of alignment. The simulations proceed as follows. For each

event, the timestamps of each RNG are shifted by 1 second with a probability α ≤ 0.5. The

average of all event z-scores is then calculated and the simulation is repeated (typically)

200 times. The fractional timestamp alignment is given by

For alignment fractions less that 50% additional shifts of -1 second and ± 2 seconds are

made as needed. Errors for the simulations are estimated as the standard error of the

simulation mean. The simulations are rather CPU intensive. The simulation for each

alignment value takes roughly 20 hours when running calculations in parallel on a four

core Intel 2.7GHz processor.

S.14 Evidence for anomalous data selection

The case for a goal-oriented effect can be strengthened by providing evidence for a model

that is consistent with SFT. One possibility mentioned in the paper is intuitive data

selection, for which psi intuition aids in selecting event parameters. In this model, the data

are not perturbed (they conform overall to the null hypothesis), but the selection of events

corresponds to times when the data naturally ﬂuctuate in the direction of hypothesis

conﬁrmation. The GCP event registration procedure allows for a test of the selection

model. Events can be divided into two subsets. One involves three event parameters: the

acceptance or rejection of a candidate event, and the setting of its start and end times. A

second subset can be identiﬁed by observing that the GCP includes 65 events that specify

24-hour periods that start and end on UTC midnight. The 24-hour speciﬁcation applies to

diffuse events, such as the Earth day celebrations, that are observed at different times and

places around the world, but do not present obvious start and end times. An candidate

event that is assigned this 24-hour designation is not subject to selection of the start and

end time parameters.

The selection model predicts different behavior for the two subsets in the proximate data

outside of the event periods. Because the GCP database includes a continuous record of

the network output, it is possible to test these predictions. The model predicts that events

that select start and end times will show an effect of opposite sign in the data lying just

outside of the designated event periods. The effect is obvious by considering a selection

procedure on random sequences of data drawn from a distribution with zero mean. A

segment of a given length is examined at different positions along the sequence and a

position that gives a positive deviation is selected. The remaining unselected data will

have a negative deviation because the sequence average is constrained to be zero. The

negative deviation will be located in the regions that were examined but not selected.

An alternate procedure models the 24-hour events. In this case whole sequences are

intermittently presented, and accepted if they deviate positively. Because proximate data

are independent and unexamined, they will not exhibit notable negative deviations. A small

negative deviation will be present in the total of all unselected data, but it will be small,

dependent on the acceptance frequency, and distributed evenly throughout the data. For

the GCP, about four of these 24-hour events are designated each year, so the small

negative effect will not be discernible from statistical noise.

falignment =↵2+(1↵2)

Cumulative deviations of the standard analysis correlation statistic for each event subset

are shown in the ﬁgures. The plots include 12 hours of data before and after the formal

event periods. The subset that selects start and end times includes 349 events with a

composite z-score of z = 5.63. The events have different durations. For visualization

purposes, the data are uniformly extended over a uniform 24 hour period by inserting zero

padding as necessary. Figure 13 shows the predicted selection effect. There are clear

negative deviations lasting for up to 8 hours both before and after the formal event period

endpoints. The extent of the deviations accurately cancels the 5.6-sigma positive deviation

of the formal events. A sharp inﬂection in the sign of the cumulative deviation curve aligns

closely with the designated period endpoints. All of these features are expected under the

selection model.

The subset of 24-hour events is shown in Figure 14 (in this case, the full data are

presented without the need for padding.). The composite z-score of the 65 events is z =

3.2. As predicted by the selection model, there are no evident negative deviations in the

data before or after the formal event periods.

Taken together, the behavior of data proximate to events is consistent with a data selection

model and this provides supporting evidence for a goal-oriented effect and SFT. Other

examinations of the proximate data are possible and further analyses are being

investigated. For example, there are events with evident start times that select primarily on

the end time alone, and vice versa. In these cases, negative deviations should be

concentrated on the selected side of the proximate data.

Figure 13. Cumulative correlation of events that freely designate event start and end times. The

black trace is the summation of 349 standard analysis events that have been uniformly

stretched over a 24-hour period in order to provide a better visualization of the data. The gray

traces are proximate data for the same events, extending 12 hours before and after event start

and end times. The curve has been shifted vertically to align the endpoints of the proximate

data with zero. The rise of the black trace corresponds to a 5.6-sigma deviation. It is entirely

cancelled by negative deviations in the proximate data, as predicted by the selection model.

Figure 14. Cumulative correlation of 24-hour events that do not select event start and end times.

The black trace is the composite of 65 events, showing a signiﬁcant positive deviation of 3.2-

sigma. Gray traces show 12 hours of proximate data before and after the event periods. The

proximate data exhibit null behavior, without detectable negative correlations, in agreement with

the selection model prediction for the 24-hour event subset.